Often times people mix models of time in order to end up with some kind of wild logically impossible sci-fi hybrid of A-theory and B-theory, which is ultimately metaphysically incoherent. We’ve all seen it being done: some show or movie or book will involve the possibility of time travel and also imply the ability to change the future by going back to the past (something which is logically impossible, and is the result of incoherent thinking altogether – at least barring some very strange conclusions about reality which I’ve explored in the John Titor post – but upon further reflection even the John Titor scenario isn’t time travel so much as world-travel). However, here’s another more subtle incoherence which often creeps into popularized time travel shows: plotlines which involve vicious circularity. By vicious circularity I mean something self-referential which lacks sufficient reason. In technical language, if P explains Q, and Q explains P, then the conjunction of P&Q remains unexplained even if both halves of the conjunct are explained. Any such self-referential explanation is going to lead to vicious circularity.
For instance, suppose that somebody from the Future comes to the Past, and tells their ‘past’ selves that they must get themselves a Ferrari. Now, while the the Future self’s having a Ferrari is explained by the Past self’s getting that Ferrari, the Past self’s getting that Ferrari is explained by the future self’s advice to get a Ferrari. The interesting question is whether such a situation is actually viciously circular. Need there be some other explanation for why the past self will get the Ferrari and why the future self has the Ferrari (the conjunct)? The only alternative is to say that the conjunct is a brute fact, and that irritates sufficient reason. Notice in this scenario it isn’t as though somebody went through some time, decided to get a Ferrari, and then went back to the past to tell themselves to get a Ferrari – there is no ‘world’ where the self who gets a Ferrari doesn’t do so precisely because her future self told her to do so. Therefore, there must be some other sufficient reason for the conjunction of those two contingent facts, such as the fact that this person freely chose to get a Ferrari at the moment she got the Ferrari, and acted as a ‘first mover’ in this restricted causal chain. Thus, the choice to get a Ferrari wasn’t determined by events prior to the choice any more than it was determined by events ‘after’ the choice, but rather the choice itself explains events both ‘after’ and prior to. So long as it is a free choice, it can fail to be entailed by past or future events, while explaining past or future events by entailing them (or in this case perhaps by acting as sufficient reason for them without entailing them, presuming that choices such as going back in time and advising the past self to get a Ferrari were also freely chosen in the Libertarian sense).
Therefore, in order for there to be a sufficient reason for a contingent and self-referential conjunct, there must be something other than the members of the conjunct which sufficiently explains the conjunct.